and the observations have to be partly carried on by stealth, and frequently with a great deal of hurry, which is very prejudicial to good work. Sometimes armed opposition or insatiable demands cannot be avoided, but are rather increased by any amount of tact and forbearance; in this case prompt and severe measures must be relied on, without regard for the opinions of those who are not fully acquainted with the circumstances, or are opposed to the success of the expedition.

These and other similar interruptions and difficulties, such as illness, breakage of instruments, loss of baggage, non-arrival of supplies, detention by floods, etc., may interfere very seriously with the work of the expedition, and render it necessary that the person to whom the survey is entrusted shall be not only capable of surveying, and taking astronomical observations, but shall also be a scientific man in other respects, a fair linguist, energetic, active, enduring, courageous, and fertile in resources and expedients.

The Traverse-work of an itinerary survey being dependent on compass-bearings and measured or estimated distances; the direction of the meridian, the magnetic variation of the compasses, and the latitude and longitude should be daily determined at starting and closing points or other stations. As observations or estimations of longitude are far less accurate than those of latitude, the more nearly the route follows a meridian, the more correct the verification; and for the same reason the checks in longitude afforded by them may frequently be disregarded, while those in latitude may not. The traverse-work should be made to involve the smallest possible number of sights, or changes of course, within practical limits, thus making

the lengths of straight course as long as possible. For measurement of distance on such routes, various forms of pedometer have to be depended on; and as for bearings two compasses should always be used to check each other for both forward and back bearings, so also for distances two pedometers should be used. As to patterns of pedometer, the wheelpedometer is good on smooth and level ground, while on rough and hilly routes it records distances in excess of the truth; the suspended or watch-pedometer, or passometer, which records the number of paces taken, gives results which have to be reduced or augmented in accordance with the nature of the ground; and the length of pace adopted under varying conditions; it is better therefore to have such instruments made to record the number of paces, than the number of miles estimated by the instrument-maker, and then suitable allowances can be made for correction, and a more correct mileage may be estimated.

In time-itineraries, where the distances are merely estimated from the recorded times of departure from and arrival at certain places or stations in the route, special attention should be paid to the variation of speed in journeying; some measurements should occasionally be taken to test it, both on the level, and on ascents and descents. The beginnings and endings of ascents and descents, also any peculiarities of the ground and circumstances affecting the speed, and halts and delays, should be invariably noted in the record; for such causes may combine to vary an otherwise equable speed by as much as a half.

Again, as the observed bearings, whether taken in degrees or more roughly in points of 1110, should fairly

represent the actual directions of the main lines traversed, it is advisable to take these when clear of a town or of any exceptional windings of route, and thus reduce errors due to such causes to a minimum. In any case, however rough the mode of estimating distance and bearing may be, the observations themselves should be correct within the capability of the means employed; otherwise the results may be valueless and unfit for reduction to plan or map.

The observations for latitude, etc., should invariably be taken with the utmost precision that the instruments admit, and as some of them are sure to be defective and necessitate rejection, the number of observations should be more than may appear exactly sufficient. The elevations of various points on or near the line of route are determined by detached observation with aneroids or hypsometers; they should be correct within 20 or 25 feet of the truth. A small amount of hill-sketching in the bolder portions of the country is also necessary, the bearings of principal peaks, passes, and marked features being taken from several points to determine their positions.

The principal cause of error in all such compass traverses is the neglect of allowances for corrections under the before-mentioned heads, also for magnetic storms, local magnetic attraction, and general diurnal or other change of magnetic variation. On some of these points. information may afterwards be obtained at the nearest magnetic observatory. The day's traverse, or run and course, should invariably be plotted daily on a sufficiently large scale on one plan, and the corrected traverse, after reduction to fit in with the observed latitudes and estimated longitudes on another. At the close of the

expedition, when further information may be forthcoming, the whole can be finally worked up to a scale on which the actual errors become invisible, thus making a final correct plan of the route.

The formulæ, and the method used in the reduction of compass traverses to a single meridian, already fully explained at page 106, are adopted in reducing the set of traverses of a day's journey to a resulting total difference of latitude, and total difference of departure in geographical miles; other formulæ in connection with geodetic arcs and latitudes are given at pages 53, 54, and exemplified at pages 63 to 66.

The following sketch of a route-survey by land comprises a portion of Thibet explored by three pan-. dits; the corresponding records Nos. VI. and VII. of the courses traversed, and the latitudes and elevations observed, are given at the end of the book. The whole has been taken from the Indian official records, as affording a better illustration of such operations in unexplored regions than anything in the author's possession or experience. The tract expiored includes an area of 18,000 square miles, the total distance traversed being 850 miles. The error in longitude amounted to only 2 minutes on the direct traverse of 160 miles.

The values of the pace used, as tested by difference of latitude, were, that of the first pandit between Badrinath and Gartok, 2'495 feet; that of the same, between Gartok and Thok-Jalung, 2′512 feet; that of the second pandit, 2634; and that of the third pandit, 2:495 feet. The observations for latitude were 190 in number, taken at 75 points. Eighty observations of altitude were also made. The check-bearings on the various mountain. peaks are omitted in the field-records issued. The

time occupied on the actual work was about five months, and from the dangerous and very trying climate and circumstances under which it was executed, it is considered one of the exploits in surveying of modern times.

In Navigation the traverse representing the vessel's course commences on leaving sight of land of known position, and closes or is checked under similar conditions; the course, or courses, are set according to two or more compasses, the direction being most generally estimated roughly in points of 1110, while for the actual true course allowance has to be made for deviation, leeway of the ship itself, winds and set of current, the estimation for these allowances requiring a knowledge of the sailing qualities of the vessel, and of the local currents at various places in various seasons; the speed of the vessel through the water is observed by means of the patent log, and to this also correction must be applied for contrary or favorable sea-drift and incidental currents, in order to obtain the actual absolute speed from time to time. The calculation or reduction of the day's set of traverses is then made as in a compass traverse (for which see page IC6), either with the aid of Gen. Boileau's well-known traverse-tables, or with a table of sines and cosines; the results taking the form of a difference of latitude and a difference of departure, both being denoted in geographical miles.

The additional calculations at sea, beyond those of the mere reduction of traverse, to differences of latitude, and departure in miles, are to obtain the difference of longitude, the day's course, or mean direction followed in the traverse, and the day's run, or distance estimated in this mean direction; these may be calculated on either of two principles, the middle latitude or the Mercatorial method.